Sen. Amy Klobuchar could be Joe Biden’s surprise veep pick — with the Democratic presidential nominee asking her to undergo rigorous vetting before potentially joining his ticket, according to a new report.

The Minnesota lawmaker, who herself ran a failed White House bid, was officially approached by Biden’s camp and is now undergoing a vetting process which will include exhaustive rounds of interviews, reviews of tax returns, speeches and potential professional or personal scandals, sources told CBS News on Thursday.

On Thursday, Rep. Val Demmings of Florida, one of the managers in President Trump’s impeachment trial in the Senate, announced she was also on a “short list.”

“I am on the short list and I am honored to be on the short list,” Demmings, a former Orange County police chief, told SiriusXM’s The Dean Obeidallah Show.

“If Vice President Biden asked me to serve along with him, I would be honored to do just that,” she added.

According to the CBS News report, several other potential women running mates are also being considered, including New Hampshire Sen. Maggie Hassan who has also agreed to be vetted.

New Hampshire’s other female senator, Jeanne Shaheen, was invited by Biden’s camp to enter the process but is up for reelection this year and declined, the report said.

Biden has committed to selecting a woman to be his vice president, sparking a fierce audition process with some female lawmakers flat-out lobbying for the job. He is reportedly considering more than a dozen candidates.

Klobuchar ran a dogged presidential bid and her moderate, Midwest-nice platform appealed to voters before the Democratic primaries moved to southern states where Biden cleaned up thanks to his support from African Americans.

One Democratic insider told The Post last month that they believed the Minnesota senator could be Biden’s number one choice, with another source praising her political skills.

The campaign is hopeful that Klobuchar can help Democrats win back the swing states of Michigan, Wisconsin, Iowa, Ohio and Pennsylvania which fell to President Trump in 2016.

California Sen. Kamala Harris and Massachusetts Sen. Elizabeth Warren have also expressed interest in the job, while former Georgia gubernatorial candidate Stacey Abrams is blatantly pushing for the gig — a move that has angered Biden insiders.